It is known in the prior art that when winding a paper web, for example when the paper web is wound in a slitter-winder, with certain paper grades, for example fine paper or liner papers, intensive oscillation peaks always occur at the same ranges of frequency of rotation of the roll irrespective of the running speed of the slitter-winder. The number of these ranges of oscillation, i.e., ranges of frequency of rotation of the roll, in which intensive oscillation occurs in the slitter-winder, is generally from 1 to 3, depending on the ultimate diameter of the roll being wound. This intensive oscillation produces winding broke, mechanical wear of the equipment, even detaching of the roll from the winding device, and often lowers the winding capacity of the winder because the running speed of the winder must be lowered during winding to avoid these detrimental effects.